I found the fix! I copied my BuddyPress Twenty Ten Child 1.0 theme, renamed it and made that the theme for my subsite. Then I went into the functions-buddypress.php file which is in the BuddyPress folder and found it's horizontal menu as shown below at line 121.
<div class="menu">
<ul>
<li<?php if ( bp_is_front_page() ) : ?> class="current_page_item"<?php endif; ?>>
<a href="<?php echo site_url() ?>" title="<?php _e( 'Home', 'buddypress' ) ?>"><?php _e( 'Home', 'buddypress' ) ?></a>
</li>
<?php if ( 'activity' != bp_dtheme_page_on_front() && bp_is_active( 'activity' ) ) : ?>
<li<?php if ( bp_is_page( BP_ACTIVITY_SLUG ) ) : ?> class="current_page_item"<?php endif; ?>>
<a href="<?php echo site_url() ?>/<?php echo BP_ACTIVITY_SLUG ?>/" title="<?php _e( 'Activity', 'buddypress' ) ?>"><?php _e( 'Activity', 'buddypress' ) ?></a>
</li>
<?php endif; ?>
<li<?php if ( bp_is_page( BP_MEMBERS_SLUG ) || bp_is_member() ) : ?> class="current_page_item"<?php endif; ?>>
<a href="<?php echo site_url() ?>/<?php echo BP_MEMBERS_SLUG ?>/" title="<?php _e( 'Members', 'buddypress' ) ?>"><?php _e( 'Members', 'buddypress' ) ?></a>
</li>
<?php if ( bp_is_active( 'groups' ) ) : ?>
<li<?php if ( bp_is_page( BP_GROUPS_SLUG ) || bp_is_group() ) : ?> class="current_page_item"<?php endif; ?>>
<a href="<?php echo site_url() ?>/<?php echo BP_GROUPS_SLUG ?>/" title="<?php _e( 'Groups', 'buddypress' ) ?>"><?php _e( 'Groups', 'buddypress' ) ?></a>
</li>
<?php if ( bp_is_active( 'forums' ) && ( function_exists( 'bp_forums_is_installed_correctly' ) && !(int) bp_get_option( 'bp-disable-forum-directory' ) ) && bp_forums_is_installed_correctly() ) : ?>
<li<?php if ( bp_is_page( BP_FORUMS_SLUG ) ) : ?> class="current_page_item"<?php endif; ?>>
<a href="<?php echo site_url() ?>/<?php echo BP_FORUMS_SLUG ?>/" title="<?php _e( 'Forums', 'buddypress' ) ?>"><?php _e( 'Forums', 'buddypress' ) ?></a>
</li>
<?php endif; ?>
<?php endif; ?>
<?php if ( bp_is_active( 'blogs' ) && bp_core_is_multisite() ) : ?>
<li<?php if ( bp_is_page( BP_BLOGS_SLUG ) ) : ?> class="current_page_item"<?php endif; ?>>
<a href="http://neighborsconnect.us/neighborhood-directory/" title="<?php _e( 'blogs', 'buddypress' ) ?>"><?php _e( 'Neighborhoods', 'buddypress' ) ?></a>
</li>
<?php endif; ?>
<?php wp_list_pages( 'title_li=&depth=1&exclude=' . bp_dtheme_page_on_front() ); ?>
<?php do_action( 'bp_nav_items' ); ?>
</ul>
</div>
I took out all the menu list items except for the Home list item and the line that provides the About Page.
<div class="menu">
<ul>
<li<?php if ( bp_is_front_page() ) : ?> class="current_page_item"<?php endif; ?>>
<a href="<?php echo site_url() ?>" title="<?php _e( 'Home', 'buddypress' ) ?>"><?php _e( 'Home', 'buddypress' ) ?></a>
</li>
<?php wp_list_pages( 'title_li=&depth=1&exclude=' . bp_dtheme_page_on_front() ); ?>
<?php do_action( 'bp_nav_items' ); ?>
</ul>
</div>
This line provides the About page:
<?php wp_list_pages( 'title_li=&depth=1&exclude=' . bp_dtheme_page_on_front() ); ?>
It works. No more BuddyPress menu items on my subsites.